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A101933 Concatenate the first n positive integers written in binary (with each integer written so the most significant 1 is on the left and the concatenated string is from left to right, A030302). a(n) is the number of times n written in binary appears disjointedly in the concatenated string.

%I A101933 #9 Sep 23 2013 08:49:09
%S A101933 1,1,2,1,2,3,3,1,2,1,4,3,4,5,4,1,2,2,3,2,2,1,6,3,4,4,6,6,5,7,5,1,2,2,
%T A101933 3,1,4,3,4,2,4,2,5,2,3,4,8,3,4,5,5,4,6,4,8,6,6,6,7,9,6,9,6,1,2,2,3,2,
%U A101933 3,3,4,2,2,3,5,2,6,4,5,2,4,3,6,3,3,3,7,2,5,3,5,3,7,5,10,3,4,5,5,4,7,5,7,4,6
%N A101933 Concatenate the first n positive integers written in binary (with each integer written so the most significant 1 is on the left and the concatenated string is from left to right, A030302). a(n) is the number of times n written in binary appears disjointedly in the concatenated string.
%C A101933 First occurrence of n: 1, 3, 6, 11, 14, 23, 30, 47, 60, 95, 126, 124, 223, 248, 252, 447, 863, 504, 895, 1008, 1020, 1016, 1919, 2044, 2032, 2040, 3839, 7159, 7871, 4080, 7679, 15855, 8160, 8184, 8176, 15839, ??, 16376, 16352, 16368, ..., to a limit of 25000.
%H A101933 Diana Mecum & Robert G. Wilson v, <a href="/A101933/b101933.txt">Table of n, a(n) for n = 1..10000</a>.
%e A101933 a(21) = 2 because 21_10 = 10101_2 and that appears in
%e A101933 1101110010111011110001001101010111100110111101111100001000110010100111010010101_2
%e A101933 three times but only two times which do not overlap.
%t A101933 a[n_] := StringCount[ ToString@ FromDigits@ Flatten@ IntegerDigits[ Range@n, 2], ToString@ FromDigits@ IntegerDigits[n, 2], Overlaps -> False]; Array[a, 105]
%Y A101933 Cf. A007088, A030190, A030302, A058935, A047778. Differs from A117127 at positions in A141439.
%K A101933 base,easy,nonn
%O A101933 1,3
%A A101933 _Diana L. Mecum_ and _Robert G. Wilson v_, Aug 31 2008